We discuss a new mechanism to enhance the spectrum of primordial tensor fluctuations in single field inflationary scenarios. The enhancement relies on a transitory non-attractor inflationary phase, which amplifies the would-be decaying tensor mode, and gives rise to a growth of tensor fluctuations at superhorizon scales. We show that the enhancement produced during this phase can be neatly treated via a tensor duality between an attractor and non-attractor phase, which we introduce. We illustrate the mechanism and duality in a kinetically driven scenario of inflation, with non-minimal couplings between the scalar and the metric.

We investigate primordial tensor non-Gaussianity in single field inflation, during a phase of nonattractor evolution when the spectrum of primordial tensor modes can be enhanced to a level detectable at interferometer scales. Making use of a tensor duality we introduced in [1], we analytically compute the full bispectrum of primordial tensor fluctuations during the non-attractor era. During this epoch the shape of the tensor bispectrum is enhanced in the squeezed limit, its amplitude can be amplified with respect to slow-roll models, and tensor non-Gaussianity can exhibit a scale dependence distinctive of our set-up. We prove that our results do not depend on the frame used for the calculations. Squeezed tensor non-Gaussianity induces a characteristic quadrupolar anisotropy on the power spectrum of the stochastic background of primordial tensor perturbations. As a step to make contact with gravitational wave experiments, we discuss the response function of a ground based Michelson interferometer to a gravitational wave background with such a feature.

We examine the validity of the classical approximation of the waterfall phase transition in hybrid inflation from an effective field theory (EFT) point of view. The EFT is constructed by integrating out the waterfall field fluctuations, up to one-loop order in the perturbative expansion. Assuming slow-roll conditions are obeyed, right after the onset of the waterfall phase, we find the backreaction of the waterfall field fluctuations to the evolution of the system can be dominant. In this case the classical approximation is completely spoiled. We derive the necessary constraint that ensures the validity of the EFT.

The focus of this work is on the topic of gravitational wave cosmology. We look for new observational signatures for primordial gravitational waves and especially for frameworks that can produce an enhanced tensor spectrum. In such cases, the gravitational wave energy density can enter within the sensitivity curves of gravi-tational wave detectors or it could leave a measurable imprint in the polarization pattern of the Cosmic Microwave Background radiation. This is very important as more sensitive, next generation experiments are expected to make indirect and direct measurements of the primordial stochastic gravitational wave background.Our investigation showed that an enhanced tensor amplitude can be achieved, within the framework of the Horndeski theory, if there is a short period where slow-roll inflation is violated. We considered a model of kinetically driven inflation where for a short time the scalar field velocity is heavily time-dependent. During that time the would-be decaying tensor mode becomes a growing mode. Analysis of the bispectrum showed that this can lead to sizeable tensor non-Gaussianities.We also considered possible realizations of the effective field theory of Scalar-Tensor gravity. In particular, we looked for a setup up of operators that could lead to the enhancement of parity violating effects for tensors. We introduced modifications to gravity which enabled us to parametrically approach the scale at which maximal parity violation occurs. Using the mathematical machinery for effective field theories we showed that sub-leading quadratic operators can become important signalling the presence of the Chern Simons instability. This inevitably implies the existence of non-trivial cubic interactions which could stand the theory strongly coupled at energies not far above the energy scale of inflation. Consequently, this can lead to large parity violation in tensor non-Gaussianity.

We construct the Effective Field Theory (EFT) of the teleparallel equivalent of general relativity (TEGR). Firstly, we present the necessary field redefinitions of the scalar field and the tetrads. Then we provide all the terms at next-to-leading-order, containing the torsion tensor and its derivatives, and derivatives of the scalar field, accompanied by generic scalar-field-dependent couplings, where all operators are suppressed by a scale Λ. Removing all redundant terms using the field redefinitions we result to the EFT of TEGR, which includes significantly more terms comparing to the EFT of General Relativity. Finally, we present an application in a cosmological framework. Interestingly enough, although GR and TEGR are completely equivalent at the level of classical equations, we find that their corresponding EFTs possess minor but non-zero differences. Hence, we do verify that at higher energies the excitation and the features of the extra degrees of freedom are slightly different in the two theories, thus making them theoretically distinguishable. Nevertheless, we mention that these differences are suppressed by the heavy mass scale Λ and thus it is not guaranteed that they could be measured in future experiments and observations.